Abe called the rescue of Japanese nationals kidnapped by Pyongyang in the 1970s and 1980s “a lifetime’s work,” according to the publication.
Five abductees returned to Japan in 2002, and Abe fought for the return of a dozen more.
North Korea, however, believes this is no longer a problem, saying eight of the 12 have died and four have never entered the country.
Abe, 65, announced on Friday that he was stepping down as the longest-serving prime minister in Japanese history due to health concerns. Abe was elected Prime Minister for the second time in December 2012, after serving a first term from 2006 to 2007.
Kim could now be “interested in whether the next Japanese prime minister will stick to the issue like Abe,” the diplomat said.
Abe recently said he would be ready to hold a summit with Kim “without conditions”, but none have ever materialized.
Kim was unwilling to meet with Abe – who has secured President Trump’s backing on the kidnapping issue – as North Korea-US negotiations over the denuclearization of the peninsula stalled, said a Japanese government source told the Japan Times.